View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by UNL | Libraries University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln US Army Research U.S. Department of Defense 2013 The modified Bruun Rule extended for landward transport J.D. Rosati U. S. Army Corps of Engineers, [email protected] R.G. Dean University of Florida T.L. Walton Coastal Tech Corp Follow this and additional works at: https://digitalcommons.unl.edu/usarmyresearch Rosati, J.D.; Dean, R.G.; and Walton, T.L., "The modified Bruun Rule extended for landward transport" (2013). US Army Research. 219. https://digitalcommons.unl.edu/usarmyresearch/219 This Article is brought to you for free and open access by the U.S. Department of Defense at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in US Army Research by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Marine Geology 340 (2013) 71–81 Contents lists available at SciVerse ScienceDirect Marine Geology journal homepage: www.elsevier.com/locate/margeo The modified Bruun Rule extended for landward transport J.D. Rosati a,⁎, R.G. Dean b, T.L. Walton c a U. S. Army Corps of Engineers, Washington, DC 20314, United States b University of Florida, Gainesville, FL 32605, United States c Coastal Tech Corp., Tallahassee, FL, United States article info abstract Article history: The Bruun Rule (Bruun, 1954, 1962) provides a relationship between sea level rise and shoreline retreat, and Received 3 January 2013 has been widely applied by the engineering and scientific communities to interpret shoreline changes and to Received in revised form 24 April 2013 plan for possible future increases in sea level rise rates. The Bruun Rule assumes that all sand removed from Accepted 28 April 2013 the upper profile is deposited offshore as sea level rises, although overwash during storms and landward Available online 13 May 2013 Aeolian transport clearly indicate otherwise. Herein, we examine processes associated with sandy beach fi Communicated by J.T. Wells evolution in response to relative sea level rise and propose a modi ed form of the Bruun Rule that considers the full range of parsing cross-shore transport, from completely seaward to completely landward depending Keywords: on the prevailing storm and surge conditions and whether there is a surplus or deficit of sand in the profile shoreline retreat with respect to the equilibrium beach profile. A methodology is proposed that more appropriately represents sea level rise the long-term processes and beach response. However, an improved quantitative understanding of landward overwash transport is required for optimal application of the proposed method. fi equilibrium beach pro le Published by Elsevier B.V. 1. Introduction Bruun Rule is the quantification of the seaward dimension of the off- shore deposition, considered as the distance from the shoreline to the The Bruun Rule (Bruun, 1954, 1962) provides a relationship depth of closure. In their consideration of an entire barrier island re- between sea level rise and shoreline retreat that, for more than five sponse to sea level rise, Dean and Maurmeyer (1983) appear to be decades, has provided the engineering and scientific communities the first to suggest both seaward and landward transport although with a useful method of interpreting shoreline changes and designing they did not discuss the issue in detail. They developed an equation beach stabilization projects, most notably beach nourishment relating barrier island retreat without a change in form to the product projects. However, attempts to verify the Bruun Rule based on field of sea level rise and the ratio of the horizontal and vertical dimensions measurements have proven quantitatively inconclusive, in part due of the active system. This translation resulted in both seaward and to noise in the data (Schwartz, 1967, 1987; Rosen, 1978; Pilkey and landward sediment transport. Dean and Maurmeyer did not provide Davis, 1987; Bruun, 1988; SCOR Working Group 89, 1991; List et al., a quantitative relationship between overwash volumes and shoreline 1997 among others). This, along with further examination of the as- retreat nor did they explicitly treat the case of overwash on a mainland sociated processes, has brought attention as to whether the Bruun as is presented herein. Rule appropriately represents evolution of sandy beaches to relative In its original form, the Bruun Rule did not consider sources and sea level. sinks nor gradients in longshore transport, although it has been mod- The Bruun Rule relates the shoreline retreat to the product of sea ified and applied to adjust for these effects. Everts (1985) developed level rise and the ratio of the horizontal to vertical dimensions of and applied a sediment budget approach which accounted for land- the active profile. The profile is translated landward and upward ward and alongshore losses as well as offshore transport due to sea without a change of form with the eroded sand from the eroded level rise. Davidson-Arnott (2005) considered landward transport upper portions of the profile transported and deposited seaward to due to shoreline response to sea level rise and further suggested raise the seaward active portions of the profile by the amount of the that all associated transport is landward. Davidson-Arnott did not sea level rise. This process, consisting only of seaward net sediment provide a relationship between shoreline retreat, sea level rise and transport, is the feature addressed herein. A key feature of the other pertinent dimensions. Herein, we examine processes associated with sandy beach evolu- tion in response to relative sea level rise and propose a modified ⁎ Corresponding author. Tel.: +1 202 761 1850. form of the Bruun Rule that considers the full range of parsing cross- E-mail address: [email protected] (J.D. Rosati). shore transport, from completely seaward to completely landward 0025-3227/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.margeo.2013.04.018 72 J.D. Rosati et al. / Marine Geology 340 (2013) 71–81 depending on the prevailing storm conditions and whether there is a Hands (1979, 1980, 1983) reported on observations of water level surplus or deficit of sand in the profile with respect to the equilibrium and associated shoreline changes on Lake Michigan from 1967 beach profile. The paper is organized by first providing a brief review of through 1976 during which the water level rose slightly more than the Bruun Rule and summarizing previous studies with a focus on field 1 m and then fell by approximately 0.2 m. Of the six surveys evaluations. We discuss fundamental concepts relating to beach re- conducted, four documented rising water level and two falling sponse and evidence demonstrating the need to modify the Bruun water level. It was found that the general characteristics of the shore- Rule for landward transport. Modified Bruun Rule equations are line response were consistent with the Bruun Rule and that the presented followed by several example calculations. We conclude by calculated recession lagged the measured recession. The calculated highlighting research and data required to apply the modified Bruun and measured shoreline changes were in good agreement at the Rule. sixth survey which documented some recovery relative to the fifth survey. 2. The Bruun Rule Rosen (1978) conducted an evaluation of the Bruun Rule based on profile response in Chesapeake Bay. The total shoreline length was The Bruun Rule relates the shoreline retreat, R, to sea level rise, S 338 km considered in 13 segments. A closure depth of 3.6 m was by the ratio of the horizontal and vertical dimensions of the active adopted for the study based on a regional slope break and earlier profile, W*, and h* + B respectively, see Fig. 1 and Eq. (1). studies showing that sand existed primarily landward of this depth. The average measured shoreline recession rates (over 100 years) for W the 13 segments were compared with those based on the Bruun R ¼ S à ð1Þ hà þ B Rule. It was found that the differences varied substantially ranging from −68% to +224%; however, the average overall agreement was within 3%. The largest differences were found in areas of marshy Additionally, the Bruun Rule predicts that all of the sand eroded shorelines. through profile retreat is transported seaward. Mimura and Nobuoka (1995) presented results from Niigata, A wide range of investigations and applications of the Bruun Rule Japan over a period of 18 years during which ground water with- and overwash have been conducted including laboratory studies drawal resulted in relative (subsidence coupled with limited sea (Schwartz, 1965, 1967; Williams, 1978; Park, 2006) and numerical level rise) sea level rise rates up to 7 cm/yr. Ninety profile lines model applications (Kobayashi et al., 1996; Tega and Kobayashi, spaced at 100 m were surveyed 11 times during the 18 year period. 2000; Donnelly et al., 2006; Donnelly, 2007, 2008; Larson et al., Closure depths of 10 m and 17.5 m were considered. Plots show 2009). SCOR Working Group 89 (1991) provided an excellent broad that the ratio of shoreline retreat to land subsidence is approximately review of the Bruun Rule and other predictive models of shoreline 100. It was concluded that the “Bruun Rule is verified to reproduce response to sea level rise. The SCOR study concluded “the existing the past shoreline retreat very well.” Subsidence complicates the laboratory and field studies have not convincingly demonstrated the evaluation of the Bruun Rule due to the reduced or no offshore depo- validity of the Bruun Rule.” Stive (2004) presented a broad and sition as shown in Fig. 2. insightful examination of the processes governing profile response Dean (1990) combined the average state-wide shoreline change to sea level rise.